The Kinematic Richness of Star Clusters - II. Stability of Spherical Anisotropic Models with Rotation

TL;DR

This paper investigates the stability of rotating, anisotropic star clusters using N-body simulations and matrix techniques, identifying key phase space regions and resonant interactions that influence bar formation.

Contribution

It combines N-body simulations with matrix methods to analyze the effects of anisotropy and rotation on bar instability in spherical stellar systems, advancing stability criteria understanding.

Findings

Identifies phase space regions most influential on bar instability.

Reveals resonant interactions significantly affect bar growth rates.

Provides insights into the relationship between frequency distribution and pattern speed.

Abstract

We study the bar instability in collisionless, rotating, anisotropic, stellar systems, using N-body simulations and also the matrix technique for calculation of modes with the perturbed collisionless Boltzmann equation. These methods are applied to spherical systems with an initial Plummer density distribution, but modified kinematically in two ways: the velocity distribution is tangentially anisotropic, using results of Dejonghe, and the system is set in rotation by reversing the velocities of a fraction of stars in various regions of phase space, a la Lynden-Bell. The aim of the N-body simulations is first to survey the parameter space, and, using those results, to identify regions of phase space (by radius and orbital inclination) which have the most important influence on the bar instability. The matrix method is then used to identify the resonant interactions in the system which have the greatest effect on the growth rate of a bar. Complementary series of N-body simulations examine these processes in relation to the evolving frequency distribution and the pattern speed. Finally, the results are synthesised with an existing theoretical framework, and used to consider the old question of constructing a stability criterion.